Collapsible hats have the advantage that they may be folded to a relatively small, compact size and shape that is easy to carry and to store. Such hats are often provided with a flat metal wire or hoop member in the outer periphery of the hat brim to give the brim a definite shape when worn. These hats are commonly collapsed by twisting the brim in such a manner that three, and only three loops are formed--much as bandsaw blades are packaged. Twisting the brim produces appreciable stresses on the wire. These stresses, of course, are undesirable because they may cause the frame to break prematurely. They also make collapsing the hat more difficult and may cause the hat to open accidentally. Further, unless expensive stainless steel is used--rusting will occur and stain and rot the fabric. In addition, this wire is "hard" and makes for a rigid package when folded.